Question -
Answer -
It is given that the energy ofthe electron beam used to bombard gaseous hydrogen at room temperature is 12.5eV. Also, the energy of the gaseous hydrogen in its ground state at roomtemperature is −13.6 eV.
When gaseous hydrogen isbombarded with an electron beam, the energy of the gaseous hydrogen becomes−13.6 + 12.5 eV i.e., −1.1 eV.
Orbital energy is related toorbit level (n) as:
For n = 3,
This energy is approximatelyequal to the energy of gaseous hydrogen. It can be concluded that the electronhas jumped from n = 1 to n = 3 level.
During its de-excitation, theelectrons can jump from n = 3 to n = 1directly, which forms a line of the Lyman series of the hydrogen spectrum.
We have the relation for wavenumber for Lyman series as:
Where,
Ry =Rydberg constant = 1.097 × 107 m−1
λ= Wavelength ofradiation emitted by the transition of the electron
For n = 3, wecan obtain λas:
If the electron jumps from n =2 to n = 1, then the wavelength of the radiation is given as:
If the transition takes placefrom n = 3 to n = 2, then the wavelength of the radiation is given as:
This radiation corresponds to theBalmer series of the hydrogen spectrum.
Hence, in Lyman series, twowavelengths i.e., 102.5 nm and 121.5 nm are emitted. And in the Balmer series,one wavelength i.e., 656.33 nm is emitted.